Multiprocessor networks with small buffers: theory and simulation

There is a rise of interest in the performance of the networks with small buffers in recent years. Analysis showed that increase in buffer size does not improved the performance in wormhole routing significantly [1--4]. Moreover, latest research proved that use of smaller buffers does not decrease the link utilization [5] for Internet routers. In interconnection networks, buffer depth of 5 packets had been shown to offer optimal performance for optical packet-switched clockwork routing [6] The use of smaller buffer sizes give some advantage in speed and possibilities to use SRAM or OPS (Optical Packet Switching). We present theoretical models and numerical results for performance of a multiprocessor network modeled as a ring of routers with small finite buffers (size 1 and 2), and with local processors that generate messages with rate λ per time slot and two output ports/buffers. Simulation results are also obtained for networks with torus topology (four output ports, total buffer capacity of 8 and 20 messages). The average queue lengths and average latency are obtained. The results show that the model of independent queues, which is valid for networks with infinite buffers, is still applicable for small λ, but breaks down, which violates the Jackson theorem.